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table of values of the Liouville function and its summatory function
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(Data Structure)
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The following table lists the values of the Liouville function $\lambda(n)$ and the summatory Liouville function $L(n)$ for $0 < n < 101$ . The Liouville function is defined as $\lambda(n) = (-1)^{\Omega(n)}$ (where $\Omega(n)$ is the number of nondistinct prime factors function). The matching summatory function for the Liouville function is $$L(n) = \sum_{i =
1}^n \lambda(i).$$
| $n$ |
$\lambda(n)$ |
$L(n)$ |
$n$ |
$\lambda(n)$ |
$L(n)$ |
$n$ |
$\lambda(n)$ |
$L(n)$ |
$n$ |
$\lambda(n)$ |
$L(n)$ |
| 1 |
1 |
1 |
26 |
1 |
0 |
51 |
1 |
$-5$ |
76 |
$-1$ |
$-8$ |
| 2 |
$-1$ |
0 |
27 |
$-1$ |
$-1$ |
52 |
$-1$ |
$-6$ |
77 |
1 |
$-7$ |
| 3 |
$-1$ |
$-1$ |
28 |
$-1$ |
$-2$ |
53 |
$-1$ |
$-7$ |
78 |
$-1$ |
$-8$ |
| 4 |
1 |
0 |
29 |
$-1$ |
$-3$ |
54 |
1 |
$-6$ |
79 |
$-1$ |
$-9$ |
| 5 |
$-1$ |
$-1$ |
30 |
$-1$ |
$-4$ |
55 |
1 |
$-5$ |
80 |
$-1$ |
$$-1$0$ \\ 6 & 1 & 0 & 31 & $-1$ & $-5$ & 56 & 1 & $-4$ & 81 & 1 & $-9$ \\ 7 & $-1$ & $-1$ & 32 & $-1$ & $-6$ & 57 & 1 & $-3$ & 82 & 1 & $-8$ \\ 8 & $-1$ & $-2$ & 33 & 1 & $-5$ & 58 & 1 & $-2$ & 83 & $-1$ & $-9$ \\ 9 & 1 & $-1$ & 34 & 1 & $-4$ & 59 & $-1$ & $-3$ & 84 & 1 & $-8$ \\ 10 & 1 & 0 & 35 & 1 & $-3$ & 60 & 1 & $-2$ & 85 & 1 & $-7$ \\ 11 & $-1$ & $-1$ & 36 & 1 & $-2$ & 61 & $-1$ & $-3$ & 86 & 1 & $-6$ \\ 12 & $-1$ & $-2$ & 37 & $-1$ & $-3$ & 62 & 1 & $-2$ & 87 & 1 & $-5$ \\ 13 & $-1$ & $-3$ & 38 & 1 & $-2$ & 63 & $-1$ & $-3$ & 88 & 1 & $-4$ \\ 14 & 1 & $-2$ & 39 & 1 & $-1$ & 64 & 1 &
$-2$ & 89 & $-1$ & $-5$ \\ 15 & 1 & $-1$ & 40 & 1 & 0 & 65 & 1 & $-1$ & 90 & 1 & $-4$ \\ 16 & 1 & 0 & 41 & $-1$ & $-1$ & 66 & $-1$ & $-2$ & 91 & 1 & $-3$ \\ 17 & $-1$ & $-1$ & 42 & $-1$ & $-2$ & 67 & $-1$ & $-3$ & 92 & $-1$ & $-4$ \\ 18 & $-1$ & $-2$ & 43 & $-1$ & $-3$ & 68 & $-1$ & $-4$ & 93 & 1 & $-3$ \\ 19 & $-1$ & $-3$ & 44 & $-1$ & $-4$ & 69 & 1 & $-3$ & 94 & 1 & $-2$ \\ 20 & $-1$ & $-4$ & 45 & $-1$ & $-5$ & 70 & $-1$ & $-4$ & 95 & 1 & $-1$ \\ 21 & 1 & $-3$ & 46 & 1 & $-4$ & 71 & $-1$ & $-5$ & 96 & 1 & 0 \\ 22 & 1 & $-2$ & 47 & $-1$ & $-5$ & 72 & $-1$ & $-6$ & 97 & $-1$ & $-1$ \\ 23 & $-1$ & $-3$ & 48 & $-1$ & $-6$ & 73
& $-1$ & $-7$ & 98 & $-1$ & $-2$ \\ 24 & 1 & $-2$ & 49 & 1 & $-5$ & 74 & 1 & $-6$ & 99 & $-1$ & $-3$ \\ 25 & 1 & $-1$ & 50 & $-1$ & $-6$ & 75 & $-1$ & $-7$ & 100 & 1 & $-2$ \\ \end{tabular} \end{document} $$ |
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"table of values of the Liouville function and its summatory function" is owned by PrimeFan.
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Cross-references: matching, function, prime factors, number, Liouville function
There is 1 reference to this entry.
This is version 1 of table of values of the Liouville function and its summatory function, born on 2008-06-04.
Object id is 10658, canonical name is TableOfValuesOfTheLiouvilleFunctionAndItsSummatoryFunction.
Accessed 464 times total.
Classification:
| AMS MSC: | 11A25 (Number theory :: Elementary number theory :: Arithmetic functions; related numbers; inversion formulas) |
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Pending Errata and Addenda
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